Having lived in Utah for 4 years I would look into Salt Lake City. Southwest will get you there. Hotels in Salt Lake City should be reasonable, and depending where you stay you should be at the ski resorts within 30-40 minutes.

Avoid Park City for cheaper lift tickets - try the SLC resorts: Brighton, Solitude, Alta (skiers only, less groomed terrain), Snowbird (more advanced terrain). Alta is nice because they have an AM pass (good for Monday before you leave).

You can get discount tickets for most or all of these places at REI in Salt Lake. You need a membership, but it's about $15 for a lifetime. You can also rent equipment there; it might be less expensive than at the resorts.